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Computer Vision · Stereo

Ruiqi Li, Yiu-ming Cheung

Recently, 3D Gaussian Splatting (3DGS) has become popular in reconstructing dense 3D representations of appearance and geometry. However, the learning pipeline in 3DGS inherently lacks the ability to quantify uncertainty, which is an important factor in applications like robotics mapping and navigation. In this paper, we propose an uncertainty estimation method built upon the Bayesian inference framework. Specifically, we propose a method to build variational multi-scale 3D Gaussians, where we leverage explicit scale information in 3DGS parameters to construct diversified parameter space samples. We develop an offset table technique to draw local multi-scale samples efficiently by offsetting selected attributes and sharing other base attributes. Then, the offset table is learned by variational inference with multi-scale prior. The learned offset posterior can quantify the uncertainty of each individual Gaussian component, and be used in the forward pass to infer the predictive uncertainty. Extensive experimental results on various benchmark datasets show that the proposed method provides well-aligned calibration performance on estimated uncertainty and better rendering quality compared with the previous methods that enable uncertainty quantification with view synthesis. Besides, by leveraging the model parameter uncertainty estimated by our method, we can remove noisy Gaussians automatically, thereby obtaining a high-fidelity part of the reconstructed scene, which is of great help in improving the visual quality.

Probabilistic Methods · Bayesian Models and Methods

Edward Milsom, Ben Anson, Laurence Aitchison

Recent work developed convolutional deep kernel machines, achieving 92.7% test accuracy on CIFAR-10 using a ResNet-inspired architecture, which is SOTA for kernel methods. However, this still lags behind neural networks, which easily achieve over 94% test accuracy with similar architectures. In this work we introduce several modifications to improve the convolutional deep kernel machine’s generalisation, including stochastic kernel regularisation, which adds noise to the learned Gram matrices during training. The resulting model achieves 94.5% test accuracy on CIFAR-10. This finding has important theoretical and practical implications, as it demonstrates that the ability to perform well on complex tasks like image classification is not unique to neural networks. Instead, other approaches including deep kernel methods can achieve excellent performance on such tasks, as long as they have the capacity to learn representations from data.

Probabilistic Methods · Bayesian Models and Methods

David Smerkous, Qinxun Bai, Fuxin Li

Particle-based Bayesian deep learning often requires a similarity metric to compare two networks. However, naive similarity metrics lack permutation invariance and are inappropriate for comparing networks. Centered Kernel Alignment (CKA) on feature kernels has been proposed to compare deep networks but has not been used as an optimization objective in Bayesian deep learning. In this paper, we explore the use of CKA in Bayesian deep learning to generate diverse ensembles and hypernetworks that output a network posterior. Noting that CKA projects kernels onto a unit hypersphere and that directly optimizing the CKA objective leads to diminishing gradients when two networks are very similar. We propose adopting the approach of hyperspherical energy (HE) on top of CKA kernels to address this drawback and improve training stability. Additionally, by leveraging CKA-based feature kernels, we derive feature repulsive terms applied to synthetically generated outlier examples. Experiments on both diverse ensembles and hypernetworks show that our approach significantly outperforms baselines in terms of uncertainty quantification in both synthetic and realistic outlier detection tasks.

Probabilistic Methods · Bayesian Models and Methods

Chu Xin Cheng, Raul Astudillo, Thomas A Desautels, Yisong Yue

We consider Bayesian algorithm execution (BAX), a framework for efficiently selecting evaluation points of an expensive function to infer a property of interest encoded as the output of a base algorithm. Since the base algorithm typically requires more evaluations than are feasible, it cannot be directly applied. Instead, BAX methods sequentially select evaluation points using a probabilistic numerical approach. Current BAX methods use expected information gain to guide this selection. However, this approach is computationally intensive. Observing that, in many tasks, the property of interest corresponds to a target set of points defined by the function, we introduce PS-BAX, a simple, effective, and scalable BAX method based on posterior sampling. PS-BAX is applicable to a wide range of problems, including many optimization variants and level set estimation. Experiments across diverse tasks demonstrate that PS-BAX performs competitively with existing baselines while being significantly faster, simpler to implement, and easily parallelizable, setting a strong baseline for future research. Additionally, we establish conditions under which PS-BAX is asymptotically convergent, offering new insights into posterior sampling as an algorithm design paradigm.

Probabilistic Methods · Bayesian Models and Methods

Dustin Wright, Christian Igel, Raghavendra Selvan

Modern neural networks are often massively overparameterized leading to high compute costs during training and at inference. One effective method to improve both the compute and energy efficiency of neural networks while maintaining good performance is structured pruning, where full network structures (e.g. neurons or convolutional filters) that have limited impact on the model output are removed. In this work, we propose Bayesian Model Reduction for Structured pruning (BMRS), a fully end-to-end Bayesian method of structured pruning. BMRS is based on two recent methods: Bayesian structured pruning with multiplicative noise, and Bayesian model reduction (BMR), a method which allows efficient comparison of Bayesian models under a change in prior. We present two realizations of BMRS derived from different priors which yield different structured pruning characteristics: 1) BMRS_N with the truncated log-normal prior, which offers reliable compression rates and accuracy without the need for tuning any thresholds and 2) BMRS_U with the truncated log-uniform prior that can achieve more aggressive compression based on the boundaries of truncation. Overall, we find that BMRS offers a theoretically grounded approach to structured pruning of neural networks yielding both high compression rates and accuracy. Experiments on multiple datasets and neural networks of varying complexity showed that the two BMRS methods offer a competitive performance-efficiency trade-off compared to other pruning methods.

Probabilistic Methods · Bayesian Models and Methods

David Huk, Yuanhe Zhang, Ritabrata Dutta, Mark Steel

Recently developed quasi-Bayesian (QB) methods \cite{fong2023martingale} proposed a stimulating change of paradigm in Bayesian computation by directly constructing the Bayesian predictive distribution through recursion, removing the need for expensive computations involved in sampling the Bayesian posterior distribution. This has proved to be data-efficient for univariate predictions, however, existing constructions for higher dimensional densities are only possible by relying on restrictive assumptions on the model's multivariate structure. Here, we propose a wholly different approach to extend Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem, by decomposing the predictive distribution into one-dimensional predictive marginals and a high-dimensional copula. We use the efficient recursive QB construction for the one-dimensional marginals and model the dependence using highly expressive vine copulas. Further, we tune hyperparameters using robust divergences (eg. energy score) and show that our proposed Quasi-Bayesian Vine (QB-Vine) is a fully non-parametric density estimator with \emph{an analytical form} and convergence rate independent of the dimension of the data in some situations. Our experiments illustrate that the QB-Vine is appropriate for high dimensional distributions ($\sim$64), needs very few samples to train ($\sim$200) and outperforms state-of-the-art methods with analytical forms for density estimation and supervised tasks by a considerable margin.

Probabilistic Methods · Gaussian Processes

Alexander Terenin, David Burt, Artem Artemev, Seth Flaxman, Mark van der Wilk, Carl Edward Rasmussen, Hong Ge

Gaussian processes are frequently deployed as part of larger machine learning and decision-making systems, for instance in geospatial modeling, Bayesian optimization, or in latent Gaussian models. Within a system, the Gaussian process model needs to perform in a stable and reliable manner to ensure it interacts correctly with other parts of the system. In this work, we study the numerical stability of scalable sparse approximations based on inducing points. To do so, we first review numerical stability, and illustrate typical situations in which Gaussian process models can be unstable. Building on stability theory originally developed in the interpolation literature, we derive sufficient and in certain cases necessary conditions on the inducing points for the computations performed to be numerically stable. For low-dimensional tasks such as geospatial modeling, we propose an automated method for computing inducing points satisfying these conditions. This is done via a modification of the cover tree data structure, which is of independent interest. We additionally propose an alternative sparse approximation for regression with a Gaussian likelihood which trades off a small amount of performance to further improve stability. We provide illustrative examples showing the relationship between stability of calculations and predictive performance of inducing point methods on spatial tasks.

Generative Models · Diffusion models

Yazid Janati, Badr MOUFAD, Alain Durmus, Eric Moulines, Jimmy Olsson

Recent advancements in solving Bayesian inverse problems have spotlighted denoising diffusion models (DDMs) as effective priors.Although these have great potential, DDM priors yield complex posterior distributions that are challenging to sample from.Existing approaches to posterior sampling in this context address this problem either by retraining model-specific components, leading to stiff and cumbersome methods, or by introducing approximations with uncontrolled errors that affect the accuracy of the produced samples.We present an innovative framework, divide-and-conquer posterior sampling, which leverages the inherent structure of DDMs to construct a sequence of intermediate posteriors that guide the produced samples to the target posterior.Our method significantly reduces the approximation error associated with current techniques without the need for retraining.We demonstrate the versatility and effectiveness of our approach for a wide range of Bayesian inverse problems.The code is available at \url{https://github.com/Badr-MOUFAD/dcps}

Probabilistic Methods · Bayesian Models and Methods

Zeyue Zhang, Xiaoling LU, Feng Zhou

The Bayesian two-step change point detection method is popular for the Hawkes process due to its simplicity and intuitiveness. However, the non-conjugacy between the point process likelihood and the prior requires most existing Bayesian two-step change point detection methods to rely on non-conjugate inference methods. These methods lack analytical expressions, leading to low computational efficiency and impeding timely change point detection. To address this issue, this work employs data augmentation to propose a conjugate Bayesian two-step change point detection method for the Hawkes process, which proves to be more accurate and efficient. Extensive experiments on both synthetic and real data demonstrate the superior effectiveness and efficiency of our method compared to baseline methods. Additionally, we conduct ablation studies to explore the robustness of our method concerning various hyperparameters.

Trustworthy Machine Learning

Qingyang Zhang, Qiuxuan Feng, Joey Tianyi Zhou, Yatao Bian, Qinghua Hu, Changqing Zhang

Out-of-distribution (OOD) detection is essential for model trustworthiness which aims to sensitively identity semantic OOD samples and robustly generalize for covariate-shifted OOD samples. However, we discover that the superior OOD detection performance of state-of-the-art methods is achieved by secretly sacrificing the OOD generalization ability. The classification accuracy frequently collapses catastrophically when even slight noise is encountered. Such a phenomenon violates the motivation of trustworthiness and significantly limits the model's deployment in the real world. What is the hidden reason behind such a limitation? In this work, we theoretically demystify the "\textit{sensitive-robust}" dilemma that lies in previous OOD detection methods. Consequently, a theory-inspired algorithm is induced to overcome such a dilemma. By decoupling the uncertainty learning objective from a Bayesian perspective, the conflict between OOD detection and OOD generalization is naturally harmonized and a dual-optimized performance could be expected. Empirical studies show that our method achieves superior performance on commonly used benchmarks. To our best knowledge, this work is the first principled OOD detection method that achieves state-of-the-art OOD detection performance without sacrificing OOD generalization ability. Our code is available at https://github.com/QingyangZhang/DUL.

Probabilistic Methods · Bayesian Models and Methods

Benjamin Feuer, Robin Schirrmeister, Valeriia Cherepanova, Chinmay Hegde, Frank Hutter, Micah Goldblum, Niv Cohen, Colin White

While tabular classification has traditionally relied on from-scratch training, a recent breakthrough called prior-data fitted networks (PFNs) challenges this approach. Similar to large language models, PFNs make use of pretraining and in-context learning to achieve strong performance on new tasks in a single forward pass. However, current PFNs have limitations that prohibit their widespread adoption. Notably, TabPFN achieves very strong performance on small tabular datasets but is not designed to make predictions for datasets of size larger than 1000. In this work, we overcome these limitations and substantially improve the performance of PFNs via context optimization. We introduce TuneTables, a parameter-efficient fine-tuning strategy for PFNs that compresses large datasets into a smaller learned context. We conduct extensive experiments on nineteen algorithms over 98 datasets and find that TuneTables achieves the best performance on average, outperforming boosted trees such as CatBoost, while optimizing fewer than 5\% of TabPFN's parameters. Furthermore, we show that TuneTables can be used as an interpretability tool and can even be used to mitigate biases by optimizing a fairness objective.

Probabilistic Methods · Gaussian Processes

Zi Wang, George Dahl, Kevin Swersky, Chansoo Lee, Zachary Nado, Justin Gilmer, Jasper Snoek, Zoubin Ghahramani

Bayesian optimization (BO) has become a popular strategy for global optimization of expensive real-world functions. Contrary to a common expectation that BO is suited to optimizing black-box functions, it actually requires domain knowledge about those functions to deploy BO successfully. Such domain knowledge often manifests in Gaussian process (GP) priors that specify initial beliefs on functions. However, even with expert knowledge, it is non-trivial to quantitatively define a prior. This is especially true for hyperparameter tuning problems on complex machine learning models, where landscapes of tuning objectives are often difficult to comprehend. We seek an alternative practice for setting these functional priors. In particular, we consider the scenario where we have data from similar functions that allow us to pre-train a tighter distribution a priori. We detail what pre-training entails for GPs using a KL divergence based loss function, and propose a new pre-training based BO framework named HyperBO. Theoretically, we show bounded posterior predictions and near-zero regrets for HyperBO without assuming the "ground truth" GP prior is known. To verify our approach in realistic setups, we collect a large multi-task hyperparameter tuning dataset by training tens of thousands of configurations of near-state-of-the-art deep learning models on popular image and text datasets, as well as a protein sequence dataset. Our results show that on average, HyperBO is able to locate good hyperparameters at least 3 times more efficiently than the best competing methods on both our new tuning dataset and existing multi-task BO benchmarks.

Generative Models · In Context Learning

Andrew Jesson, Nicolas Beltran Velez, Quentin Chu, Sweta Karlekar, Jannik Kossen, Yarin Gal, John Cunningham, David Blei

This paper presents a method for estimating the hallucination rate for in-context learning (ICL) with generative AI. In ICL, a conditional generative model (CGM) is prompted with a dataset and a prediction question and asked to generate a response. One interpretation of ICL assumes that the CGM computes the posterior predictive of an unknown Bayesian model, which implicitly defines a joint distribution over observable datasets and latent mechanisms. This joint distribution factorizes into two components: the model prior over mechanisms and the model likelihood of datasets given a mechanism. With this perspective, we define a \textit{hallucination} as a generated response to the prediction question with low model likelihood given the mechanism. We develop a new method that takes an ICL problem and estimates the probability that a CGM will generate a hallucination. Our method only requires generating prediction questions and responses from the CGM and evaluating its response log probability. We empirically evaluate our method using large language models for synthetic regression and natural language ICL tasks.

Probabilistic Methods · Bayesian Models and Methods

Marco Miani, Lorenzo Beretta, Søren Hauberg

Current uncertainty quantification is memory and compute expensive, which hinders practical uptake. To counter, we develop Sketched Lanczos Uncertainty (SLU): an architecture-agnostic uncertainty score that can be applied to pre-trained neural networks with minimal overhead. Importantly, the memory use of SLU only grows logarithmically with the number of model parameters. We combine Lanczos' algorithm with dimensionality reduction techniques to compute a sketch of the leading eigenvectors of a matrix. Applying this novel algorithm to the Fisher information matrix yields a cheap and reliable uncertainty score. Empirically, SLU yields well-calibrated uncertainties, reliably detects out-of-distribution examples, and consistently outperforms existing methods in the low-memory regime.

Language

Chaeyun Jang, Hyungi Lee, Jungtaek Kim, Juho Lee

Fine-tuning pre-trained models for downstream tasks is a widely adopted technique known for its adaptability and reliability across various domains. Despite its conceptual simplicity, fine-tuning entails several troublesome engineering choices, such as selecting hyperparameters and determining checkpoints from an optimization trajectory. To tackle the difficulty of choosing the best model, one effective solution is model fusion, which combines multiple models in a parameter space. However, we observe a large discrepancy between loss and metric landscapes during the fine-tuning of pre-trained language models. Building on this observation, we introduce a novel model fusion technique that optimizes both the desired metric and loss through multi-objective Bayesian optimization. In addition, to effectively select hyperparameters, we establish a two-stage procedure by integrating Bayesian optimization processes into our framework. Experiments across various downstream tasks show considerable performance improvements using our Bayesian optimization-guided method.

Yibo Miao, Hongcheng Gao, Hao Zhang, Zhijie Deng

The detection of machine-generated text, especially from large language models (LLMs), is crucial in preventing serious social problems resulting from their misuse. Some methods train dedicated detectors on specific datasets but fall short in generalizing to unseen test data, while other zero-shot ones often yield suboptimal performance. Although the recent DetectGPT has shown promising detection performance, it suffers from significant inefficiency issues, as detecting a single candidate requires querying the source LLM with hundreds of its perturbations. This paper aims to bridge this gap. Concretely, we propose to incorporate a Bayesian surrogate model, which allows us to select typical samples based on Bayesian uncertainty and interpolate scores from typical samples to other samples, to improve query efficiency. Empirical results demonstrate that our method significantly outperforms existing approaches under a low query budget. Notably, when detecting the text generated by LLaMA family models, our method with just 2 or 3 queries can outperform DetectGPT with 200 queries.

Chuanyang Jin, Yutong Wu, Jing Cao, Jiannan Xiang, Yen-Ling Kuo, Zhiting Hu, Tomer Ullman, Antonio Torralba, Joshua Tenenbaum, Tianmin Shu

Theory of Mind (ToM), the ability to understand people’s mental states, is an essential ingredient for developing machines with human-level social intelligence. Recent machine learning models, particularly large language models, seem to show some aspects of ToM understanding. However, existing ToM benchmarks use unimodal datasets – either video or text. Human ToM, on the other hand, is more than video or text understanding. People can flexibly reason about another person’s mind based on conceptual representations (e.g., goals, beliefs, plans) extracted from any available data. To address this, we introduce a multimodal Theory of Mind question answering (MMToM-QA) benchmark. MMToM-QA comprehensively evaluates machine ToM both on multimodal data and on different kinds of unimodal data about a person’s activity in a household environment. To engineer multimodal ToM capacity, we propose a novel method, BIP-ALM (Bayesian Inverse Planning Accelerated by Language Models). BIP-ALM extracts unified representations from multimodal data and utilizes language models for scalable Bayesian inverse planning. We conducted a systematic comparison of human performance, BIP-ALM, and state-of-the-art models, including GPT-4. The experiments demonstrate that large language models and large multimodal models still lack robust ToM capacity. BIP-ALM, on the other hand, shows promising results, by leveraging the power of both model-based mental inference and language models.

Alexis Ross, Jacob Andreas

When a teacher provides examples for a student to study, these examples must be informative, enabling a student to progress from their current state toward a target concept or skill. Good teachers must therefore simultaneously infer what students already know and adapt their teaching to students’ changing state of knowledge. There is increasing interest in using computational models, particularly large language models, as pedagogical tools. As students, language models in particular have shown a remarkable ability to adapt to new tasks given small numbers of examples. But how effectively can these models adapt as teachers to students of different types? To study this question, we introduce a suite of models and evaluation methods we call AdapT. AdapT has two components: (1) a collection of simulated Bayesian student models that can be used for evaluation of automated teaching methods; (2) a platform for evaluation with human students, to characterize the real-world effectiveness of these methods. We additionally introduce (3) AToM, a new probabilistic method for adaptive teaching that jointly infers students’ past beliefs and optimizes for the correctness of future beliefs. In evaluations of simulated students across three learning domains (fraction arithmetic, English morphology, function learning), AToM systematically outperforms LLM-based and standard Bayesian teaching methods. In human experiments, both AToM and LLMs outperform non-adaptive random example selection. Our results highlight both the difficulty of the adaptive teaching task and the potential of learned adaptive methods for solving it.

Wangtao Sun, Haotian Xu, Xuanqing Yu, Pei Chen, Shizhu He, Jun Zhao, Kang Liu

Although Large Language Models (LLMs) are showing impressive performance on a wide range of Natural Language Processing tasks, researchers have found that they still have limited ability to conduct induction. Recent works mainly adopt “post processes” paradigms to improve the performance of LLMs on induction (e.g., the hypothesis search & refinement methods), but their performance is still constrained by the inherent inductive capability of the LLMs. In this paper, we propose a novel framework, Induction through Deduction (ItD), to enable the LLMs to teach themselves induction through deduction. The ItD framework is composed of two main components: a Deductive Data Generation module to generate induction data and a Naive Bayesian Induction module to optimize the fine-tuning and decoding of LLMs. Our empirical results showcase the effectiveness of ItD on two induction benchmarks, achieving relative performance improvement of 36% and 10% compared with previous state-of-the-art, respectively. Our ablation study verifies the effectiveness of two key modules of ItD. We also verify the effectiveness of ItD across different LLMs and deductors. The data and code of this paper can be found at https://github.com/forangel2014/ItD.

Applications · Chemistry and Drug Discovery

Agustinus Kristiadi, Felix Strieth-Kalthoff, Marta Skreta, Pascal Poupart, Alan Aspuru-Guzik, Geoff Pleiss

Automation is one of the cornerstones of contemporary material discovery. Bayesian optimization (BO) is an essential part of such workflows, enabling scientists to leverage prior domain knowledge into efficient exploration of a large molecular space. While such prior knowledge can take many forms, there has been significant fanfare around the ancillary scientific knowledge encapsulated in large language models (LLMs). However, existing work thus far has only explored LLMs for heuristic materials searches. Indeed, recent work obtains the uncertainty estimate---an integral part of BO---from point-estimated, _non-Bayesian_ LLMs. In this work, we study the question of whether LLMs are actually useful to accelerate principled _Bayesian_ optimization in the molecular space. We take a sober, dispassionate stance in answering this question. This is done by carefully (i) viewing LLMs as fixed feature extractors for standard but principled BO surrogate models and by (ii) leveraging parameter-efficient finetuning methods and Bayesian neural networks to obtain the posterior of the LLM surrogate. Our extensive experiments with real-world chemistry problems show that LLMs can be useful for BO over molecules, but only if they have been pretrained or finetuned with domain-specific data.